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Thanks! For convex sets of distributions: If you weaken the definition of fixed point to , then the set has a least element which really is a least fixed point.
Hyperbolic growth
The differential equation , for positive and , has solution
(after changing the units). The Roodman report argues that our economy follows this hyperbolic growth trend, rather than an exponential one.
While exponential growth has a single parameter — the growth rate or interest rate — hyperbolic growth has two parameters: is the time until singularity, and is the "hardness" of the takeoff.
A value of close to zero gives a "soft" takeoff where the derivative gets high well in advance of the singularity. A large value of gives a "hard" takeoff, where explosive growth comes all at once right at the singularity. (Paul Christiano calls these "slow" and "fast" takeoff.)
Paul defines "slow takeoff" as "There will be a complete 4 year interval in which world output doubles, before the first 1 year interval in which world output doubles." This corresponds to . (At , the first four-year doubling starts at and the first one-year doubling starts at years before the singularity.)
So the simple hyperbola with counts as "slow takeoff". (This is the "naive model" mentioned in footnote 31 of Intelligence Explosion Microeconomics.)
Roodman's estimates of historical are closer to (see Table 3).
Ah, beginning-of-line-text is nice. It skips over the initial # or // of comments and the initial * of Org headings. I've now bound it to M-m.
Consider seeing a doctor about the panicky and stressed feelings. They may test you for hormone imbalances or prescribe you antianxiety medication.
A long reflection requires new institutions, and creating new institutions requires individual agency. Right? I have trouble imagining a long reflection actually happening in a world with the individual agency level dialed down.
A separate point that's perhaps in line with your thinking: I feel better about cultivating agency in people who are intelligent and wise rather than people who are not. When I was working on agency-cultivating projects, we targeted those kinds of people.
What's more, even selfish agents with de dicto identical utility functions can trade: If I have two right shoes and you have two left shoes, we'd trade one shoe for another because of decreasing marginal utility.
1Recent interviews with Eliezer:
- 2023.02.20 Bankless
- 2023.02.20 Bankless followup
- 2023.03.11 Japan AI Alignment Conference
- 2023.03.30 Lex Fridman
- 2023.04.06 Dwarkesh Patel
- 2023.04.18 TED talk
- 2023.04.19 Center for the Future Mind
- 2023.05.04 Accursed Farms
- 2023.05.06 Logan Bartlett
- 2023.05.06 Fox News
- 2023.05.08 EconTalk
- 2023.07.02 David Pakman
- 2023.07.13 AI IRL
- 2023.07.13 The Spectator (Edited transcript of the full interview)
- 2023.07.13 Dan Crenshaw
- 2023.07.28 Coleman Hughes (with Scott Aaronson and Gary Marcus)
- 2023.08.16 Dwarkesh Patel (with George Hotz)
- 2023.08.23 One Decision
- 2023.09.23 Destiny
The bug patches / epiphanies / tortoises / wizardry square from Small, Consistent Effort: Uncharted Waters In the Art of Rationality
Another example is the obfuscated arguments problem. As a toy example:
Even if the conclusion of the argument is a lie, each premise is spot-checkable and most likely true. The lie has been split up into many statements each of which is only slightly a lie.